Algebraic Fractions
The same rules apply for algebraic fractions as for normal fractions

When adding or subtracting, make a common denominator.

When multiplying fractions, cross cancel first if possible. Multiply the denominators together to make a new denominator. Multiply the numerators together to make a new numerator. Cancel if possible.

When dividing fractions, invert the dividing fraction and multiply.
Example: Add and simplify
Notice first thatfactorises intoThe question becomes
Example: Add and simplify if possible:
No further simplification is possible.
Example: Multiplyby
factorises:
Hence
since theandterms cross cancel.
Example: Divideby
factorises:Hence
Since theterms cross cancel.